http://physics.colorado.edu/phys3070Conduction heat transferDegree-daysConduction through a wallConduction through a wallHeat losses by conductionEnergy and TemperatureLowering the thermostatEnergy loss vs. temperatureHot waterTypical hot water heaterEnergy lossesCost/benefitCost/benefitHigh-efficiency lightingRecyclingJudah Levine, 3070L27 1http://physics.colorado.edu/phys3070http://physics.colorado.edu/phys3070Judah LevineJudah LevineJILA SJILA [email protected]@colorado.edu303 492303 492--7785 (27785 (2--7785)7785)M,F 11M,F 11--Noon, W 1Noon, W 1--3 pm3 pmalso by appointmentalso by appointmentJudah Levine, 3070L27 2Conduction heat transferConduction heat transfer()LHTTARtQ−=1BTU/hrFahrenheit degreesSquare feet⎟⎟⎠⎞⎜⎜⎝⎛••BTUftFhr2degJudah Levine, 3070L27 3DegreeDegree--daysdays()tTTARQLH−=1Average difference between outside temperature andstandard inside temperature of 65Fprovides a rough measure of heating requirementsJudah Levine, 3070L27 4Conduction through a wallConduction through a wallExterior siding, R=0.81Plywood, R=0.94Insulation R=10.9Plasterboard, R=0.45Total, R=13.1ExteriorsidingInterior plasterboard2×4+insulationplywoodJudah Levine, 3070L27 5Conduction through a wallConduction through a wallR= 13.1A= 8 ft × 12 ft = 96 ft2()hrBTUtQ3152568961.131=−××=Judah Levine, 3070L27 6Heat losses by conductionHeat losses by conductionWall, no insulation= 1160 BTU/hrWall, insulation = 315 BTU/hrWindow = 391 BTU/hr(1 Air change = 4575 BTU)Typical house has 0.5-1 per hourLow loss windows:www.energystar.govJudah Levine, 3070L27 7Energy and TemperatureEnergy and TemperatureTCQ∆=∆For any object:DegreesBTUs,calories,…Mass andtype ofmaterial∆Q= Energy input or output∆T = Change in temperatureCQT∆=∆Make C as large as possibleJudah Levine, 3070L27 8Lowering the thermostatLowering the thermostatFirst case: Leave thermostat set at 75 for time t:()tconstempinsidetTRQLtan751=−=Second case: reduce thermostat to 65 for time t:CdQTTdtTTRdQHLH−=∆−=−=7575)(1Judah Levine, 3070L27 9Energy loss vs. temperatureEnergy loss vs. temperatureQQSimplification: consider loss at both endSimplification: consider loss at both end--point point temperatures:temperatures:()()8.050402575256525751256517565==−−=−−=tRtRQQLowering inside temperature reduces the rate of heat lossJudah Levine, 3070L27 10Hot water Hot water Hot water temperature= 140FCold water temperature= 40FEfficiency= 60% (?)gallonBTUgallonBTUFgallonpoundsgallonBTUQ 13836.018301003.8 =×=×=Shower= 20 gallons= about 27,670 BTU=0.28 therm= $0.28+ Energy losses30 showers/month=$8.40Judah Levine, 3070L27 11Typical hot water heaterTypical hot water heater40 gallons (about 2+ showers) 40,000 BTU/hrEfficiency= 60%Temperature rise= 100FhrhrBTUBTUtimehrBTUeffhrBTUBTUpoundBTUgallonpoundsgallons4.1/000,24200,33000,246.0000,40200,331003.840===×=××Judah Levine, 3070L27 12Energy lossesEnergy lossesHot exhaustHeat leaks into surroundings:Conduction through outer surface:2πRL+2πR2 ≅ 2πRLLCapacity~πR2LCombustion airGas inJudah Levine, 3070L27 13Judah Levine, 3070L27 14Judah Levine, 3070L27 15Cost/benefitCost/benefit“Best” conventional tank heater= $378Tank-less heater = $999Extra cost= $621Savings claim= 30% of cost of hot water0.3×$30= $9/month= $108/yearCost Recovery period 69 months or about 6 yearsJudah Levine, 3070L27 16Cost/benefitCost/benefit“Best” conventional tank heater= $378Tank-less heater = $999Extra cost= $621Savings claim= 30% of cost of hot water0.3×$30= $9/month= $108/yearCost Recovery period 69 months or about 6 yearsSavings bond pays 5% = $31/yearNet savings= $ 77/yearCost Recovery period 8+ years108/621 is about 18%Judah Levine, 3070L27 17HighHigh--efficiency lightingefficiency lighting13watt high efficiency light = 65 watt standard incandescentSaving about 52 watts × 10,000 hours= 520,000 watt-hoursCost saving 520 kWh= $52Total hardware cost about the same:10 incandescent vs. 1 high-efficiencyRecovery time = ?10,000 hours= 4 hours/day for 6.8 yearsJudah Levine, 3070L27 18RecyclingRecyclingQQAluminum cansAluminum cansQQResidential cost about $10 per monthResidential cost about $10 per
View Full Document